Isotropic tensor valued functions of tensor arguments play an important role in the formulation of the equations governing the behavior of solid materials in the field of continuum mechanics. When the tensor argument is non-symmetric, the complexity and the difficulty in dealing with the tensor functions are high. In this work, the issue of expressing an isotropic tensor valued tensor function of a non-symmetric tensor argument is attention by utilizing the Dunford-Taylor integral. An important subclass of the isotropic tensor functions is considered with the commutative property.